Factor completely. $25+70x+49x^2=$
Solution: Both $25$ and $49x^2$ are perfect squares, since $25=({5})^2$ and $49x^2=({7x})^2$. Additionally, $70x$ is twice the product of the roots of $25$ and $49x^2$, since $70x=2({5})({7x})$. $25+70x+x^2 = ({5})^2+2({5})({7x})+({7x})^2$ So we can use the square of a sum pattern to factor: ${a}^2 +2( a)( b)+ {b}^2 =({a}+{b})^2$ In this case, ${a}={5}$ and ${b}={7x}$ : $ ({5})^2+2({5})({7x})+({7x})^2 =({5}+{7x})^2$ In conclusion, $25+70x+49x^2=(5+7x)^2$ Remember that you can always check your factorization by expanding it.